Solution:
Since dn has at least n+1 digits for any d≥10, we need only consider 1 through 9. If dn has fewer than n digits, every higher power of d will also be too small since d < 10. We will also never have n+1 digits for our nth powers. All we have to do is check dn for each d in {1,...,9}, trying n=1,2,... and stopping when dn has fewer than n digits.